Biblioteca de la Universidad Complutense de Madrid

On convex polyhedra as regular images of R(n)

Impacto

Fernando Galván, José Francisco y Gamboa, J. M. y Ueno, Carlos (2011) On convex polyhedra as regular images of R(n). Proceedings of the London Mathematical Society , 103 . pp. 847-878. ISSN 0024-6115

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URL Oficial: http://plms.oxfordjournals.org/content/103/5/847.full.pdf+html




Resumen

We show that convex polyhedra in R(n) and their interiors are images of regular maps R(n) -> R(n). As a main ingredient in the proof, given an n-dimensional, bounded, convex polyhedron K subset of R(n) and a point p is an element of R(n) \ K, we construct a semialgebraic partition {A, B, T} of the boundary partial derivative K of K determined by p, and compatible with the interiors of the faces of K, such that A and B are semialgebraically homeomorphic to an (n - 1)-dimensional open ball and J is semialgebraically homeomorphic to an (n - 2)-dimensional sphere. Finally, we also prove that closed balls in R n and their interiors are images of regular maps R(n) -> R(n).


Tipo de documento:Artículo
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:15062
Referencias:

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G. Stengle, ‘A Nullstellensatz and a Positivstellensatz in semialgebraic geometry’, Math. Ann. 207 (1974)87–97.

8. C. Ueno, ‘On convex polygons and their complementaries as images of regular and polynomial maps of R2’,Preprint, RAAG, Fuerteventura: 2009.

Depositado:03 May 2012 09:16
Última Modificación:01 Mar 2016 16:15

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